A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or

ID: 3133513 • Letter: A

Question

A fair coin is tossed 12 times. Which of the following outcomes (i, ii, iii, or iv) is most likely?

A. (i) because there are an equal number of heads and tails.

B. (ii) because there are an equal number of heads and tails but in a random order

C. (iii) because heads are just as likely as tails

D. (iv) because you won’t necessarily get the same number of heads and tails with a fair coin

E. They are all equally likely.

(i) H T H T H T H T H T H T (ii) H T T H H T T H T H H T (iii) H H H H H H H H H H H H (iv) T T T H T H H H H T H H

E. They are all eqully likely.

For fair coin P(H)=0.5 P(T)=0.5

Consider a 2 fair coin case

all possibilities are

HH prob= 0.5*0.5 =0.25 =1/4

HT prob= 0.5*0.5 =0.25 =1/4

TH prob= 0.5*0.5 =0.25 =1/4

TT prob= 0.5*0.5 =0.25 =1/4

As you see probability of each outcome. They are all same

so they are equally likely

This goes same for the 12 fair coin case

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.